Season 1, episode 1.
Original air date: 4 October 1949.
Cast: Marie Blake (Dian Fauntelle), John Brown (Digby `Digger` O`Dell), Rosemary DeCamp (Peg Riley). Marlo Dwyer (Hary Harvey), Jackie Gleason (Charles A. Riley), Lanny Rees (Junior Riley), Sib Tomack (Jim Gillis) and Gloria Winters (Babs Riley).
From IMDB.

Background Info From Wiki:
Originally, William Bendix was to have appeared on both radio and television, but Bendix's RKO movie contract prevented him from appearing on TV. Instead, Jackie Gleason starred, along with Rosemary DeCamp as wife Peg, Gloria Winters as daughter Barbara (Babs), Lanny Rees as son Chester Jr. (Junior), and Sid Tomack as Jim Gillis, Riley's manipulative best buddy and next-door neighbor. One of the William Bendix film commitments that kept him from bringing Chester Riley to television the first time around was a 1949 film version of The Life of Riley itself.
Television's first Life of Riley won television's first Emmy (for "Best Film Made For and Shown on Television"). However, it came to an end on March 28, 1950 after 26 episodes, but not because of "low ratings" or a desire by Gleason to leave the series, as previously assumed; the real reason was that Irving Brecher and sponsor Pabst Brewing Company reached an impasse on extending the series for a full 39-week season. The second TV series, produced by Tom McKnight for NBC, brought back William Bendix, beginning January 2, 1953 on NBC.
This plot was used again and can be seen here on the IA at:
http://www.archive.org/details/life_of_riley_-_1x17_-_rileys_operation

Warning: Teh Review contains some spelling errors, grammar mistakes...

Another of those "Life of Riley" uploads by uploaded "Lum", this is an entertaining episode, even if it is obviously edited with some scenes deleted (a common problem with the prints that circulate for syndication).

Regardless, this storyline could easily still work today.